Estimation and Validation of the “c” Factor for Overall Cerebral Functioning in the Philadelphia Neurodevelopmental Cohort

Abstract

While both psychopathology and cognitive deficits manifest in mental health disorders, the nature of their relationship remains poorly understood. Recent research suggests a potential common factor underlying both domains. Using data from the Philadelphia Neurodevelopmental Cohort (N = 9494, ages 8–21), we estimated and validated a “c” factor representing overall cerebral functioning through a structural model combining cognitive and psychopathology indicators. The model incorporated general factors of psychopathology (“p”) and cognitive ability (“g”), along with specific sub-domain factors. We evaluated the model’s criterion validity using external measures, including parent education, neighborhood socioeconomic status, global functioning, and intracranial volume, and assessed its predictive utility for longitudinal psychosis outcomes. The model demonstrated acceptable fit (CFI = 0.98, RMSEA = 0.021, SRMR = 0.030), and the “c” factor from this model showed stronger associations with parent education (r = 0.43), neighborhood SES (r = 0.47), and intracranial volume (r = 0.39) than “p” and “g” factors alone. Additionally, baseline “c” factor scores significantly predicted psychosis spectrum outcomes at follow-up (d = 0.30–0.57). These findings support the utility of a “c” factor in capturing overall cerebral function across cognitive and psychopathology domains, with potential implications for understanding brain function, improving clinical assessment, and optimally focusing interventions.

1. Introduction

Psychopathology and cognitive deficits are the two behavioral manifestations of mental health disorders that impact functional outcomes, yet understanding how they relate to each other and additively or interactively contribute to outcome is still rudimentary [1]. Most studies have examined either psychopathology alone [2,3,4,5] or cognition alone [6,7,8], and few examined associations among psychopathology and neurocognitive domains cross-diagnostically (but see [9,10,11]). Both classes of behavior comprise multiple sub-domains with specific characteristics. Thus, psychopathology includes symptom clusters such as those seen in depression [12], psychosis [13], and conduct disorder [14], while cognition includes abilities such as executive control [15] and episodic memory [16]. Of note, sub-domains of both cognition and psychopathology correlate with each other within super-domains—i.e., measures of psychopathology correlate with other measures of psychopathology, and measures of cognition correlate with other measures of cognition —suggesting hierarchical structures of each, whereby higher-order phenomena influence all sub-domains. In cognition, the positive correlation among all ability tests is thought to be caused by a “g” factor of “general” abilities [17,18]. In psychopathology, the positive correlation among all symptoms and diagnoses has become known as the “p” factor [19,20].

As both cognition and psychopathology are products of brain processes, it is reasonable to expect that indicators of each would correlate not only within but across super-domains [21]. It is therefore worthwhile to seek a common cause for both high psychopathology and low cognitive ability. Perhaps the first effort toward this end was conducted by [22] in their modeling of the “Big Everything” factor. These investigators examined the overlap among common factors in psychopathology, personality, pathological personality, and cognitive functioning using longitudinal data from a sample of college students, finding substantial overlap among general factors of psychopathology (p), personality (GFP), and pathological personality (GFPP). They demonstrated that a “Big Everything” factor accounted for considerable variance across these domains, but not cognitive functioning; further, they cautioned against overinterpreting these results, highlighting limitations of factor analytic approaches and bifactor models in determining the structure of psychological constructs.

Recently, [23] proposed a similar model, with a single overarching factor explaining correlations among all cognitive and psychopathology indicators, beyond what is explained by “g” and “p”. They termed this super-ordinate factor “c” for “cerebral function”, which places equal emphasis on cognitive and clinical aspects of “c”. Notably, Fissler et al. [23] did not estimate the “c” factor in a data set, but rather presented a theory and framework for how “c” could be modeled and provided suggestions for how that model could be validated. Here, we take that further step and estimate and validate a “c” factor in a large, well-studied data set, the Philadelphia Neurodevelopmental Cohort [13].

Configuration of the c-factor model is “tri-factor” [24] in that each variable loads on the following three factors simultaneously:

• Its own specific factor (e.g., verbal memory test on the “Memory” factor);
• The general factor comprising variables in its super-domain (e.g., verbal memory test on the “g” factor);
• The c-factor comprising all variables.

Both cognitive and clinical variables have been conceptualized as bifactor [25] configurations, the “p” factor [20] and “g” factor [18,26], respectively, and the c-factor combines those two bifactor models into a single model with a super-ordinate factor encompassing both “g” and “p”. The model tests whether the apparent hierarchical structures of psychopathology and cognition might not “top out” at “p” and “g”, but rather these might themselves be sub-factors in a yet higher-order phenomenon termed “c”. Tri-factor modeling was developed to address a fundamental limitation in analyzing multi-informant data, where traditional approaches struggled to separate shared variance across raters from unique rater perspectives and trait-specific components. This methodological advancement is particularly valuable when researchers need to model three distinct sources of variation simultaneously, and unlike bifactor models that can partition variance into only two components, tri-factor models allow researchers to examine how much variance in observed scores is attributable to a general factor, a second general factor, and specific content domains, providing a more nuanced understanding of complex measurement structures. This makes tri-factor modeling an excellent fit for the current study, where we have exactly three sources of variance to explain.

Parsing levels of cerebral phenomena, from the specific (e.g., depression or episodic memory) to the super-domain (“p”, “g”, and maybe others to be uncovered) to the highest-order (“c”), is an essential step toward precision psychiatry [27]. As pointed out by Fissler et al. [23], establishing a c factor “may transform many areas of research and clinical practice …[and] help to reveal the respective biological and psychosocial determinants that can be tackled using personalized and evidence-based treatments.” (p. 15). The goals of the present study were to, (1) in a large community sample, model the relationships among cognitive and psychopathology indicators using a tri-factor structural measurement model, (2) examine how factor scores calculated from this model relate to external demographic and biological criteria, and (3) evaluate whether the c factor helps predict functional outcome in a follow-up sample.

Before describing the study, it is worth noting that factor analysis in psychiatric research presents several methodological challenges that warrant careful consideration, and some of these are further elaborated in the Discussion. The selection of variables to include can substantially impact the resulting factor structure, potentially leading to both under- and over-extraction of factors if symptoms or domains are not comprehensively sampled. Another critical consideration is sample heterogeneity: factor structures derived from one population (e.g., community samples) may not generalize to others (e.g., clinical populations), and developmental changes in symptom presentation can lead to different factor structures across age groups. Relatedly, factor analysis typically assumes measurement invariance across other groupings (e.g., gender), an assumption that may not hold in psychiatric data where symptom meaning and severity can vary across cultural contexts or disease stages. These methodological challenges underscore the importance of careful study design, appropriate statistical approaches, and cautious interpretation of factor analytic results in psychiatric research.

2. Materials and Methods

2.1. Participants

Participants in this study were from the Philadelphia Neurodevelopmental Cohort (PNC), which has been described in detail elsewhere [13]. Briefly, the PNC is a community sample of N = 9494 individuals age 8–21 years (mean = 14.2), 51.7% female, 55.8% European American, 32.9% African American, from the greater Philadelphia area.

Table 1. Clinical diagnostic rates and demographic characteristics of sample at baseline.

Characteristic	Mean or Proportion	N with Valid Data
Mean Age, years (SD)	14.2 (3.7)	9488
Proportion Female	0.52	9494
Proportion European-American	0.56	9494
Proportion African-American	0.33	9494
Mean Parent * Edu, years (SD)	14.3 (2.3)	9392
Mean C-GAS (SD)	79.2 (12.0)	9331
Mean PRIME Total (SD)	5.6 (10.0)	9411
Depression	0.12	9411
Generalized Anxiety	0.03	9411
Halluc./Delus. †	0.04	9411
Mania	0.01	9411
Separation Anxiety	0.05	9411
Specific Phobia	0.33	9411
Social Phobia/Anxiety	0.21	9411
Panic Disorder	0.01	9411
Agoraphobia	0.05	9411
PTSD	0.11	9411
Obsessive Compulsive	0.03	9411
Attention Deficit Hyperactivity	0.18	9411
Oppositional Defiant	0.30	9411
Conduct	0.06	9411

Note. SD = standard deviation; Edu = education. * Parent education was calculated as the mean of the two parents’ years of education, but if one parent’s data were missing, the non-missing parent’s value was used; † Halluc./Delus. indicates possible or definite hallucinations or delusions based on K-SADS screen, with duration ≥1 day, occurring outside the context of substance, illness, and medicines, and accompanied by significant impairment or distress (rating ≥ 5).

shows the demographic characteristics and clinical diagnosis rates for the sample at baseline. As expected in a community sample, rates of clinical diagnoses in this age range mostly reflect national rates.

2.2. Cognitive Measures: Penn Computerized Neurocognitive Battery (CNB)

The tests in the CNB measure the following neurocognitive domains: Executive Control, Episodic Memory, Complex Cognition, and Social Cognition. The tests are briefly described below, as they have been extensively detailed in earlier publications [28,29].

2.2.1. Executive Control

Abstraction and Mental Flexibility (ABF) measured by The Penn Conditional Exclusion Test [30]. Participants must determine which object in a group does not belong. The exclusion rule can be based on the shape or configuration of the objects (e.g., a square would not fit in with three stars), the size of the objects, or the thickness of the lines outlining the objects. The participant is given feedback (“correct” or “incorrect”) after each response, and the test-administration program automatically changes the exclusion rule after 10 consecutively correct responses (without informing the participant). The participant must then use the feedback to determine what the new exclusion rule is, and after 10 consecutively correct responses, the rule is changed again. The test is scored based on demonstrated learning (proportion of correct responses multiplied by the number of learned rules; 1 is added to accommodate participants who were unable to discover any rule). Note that while this test was originally developed to measure executive functioning, in analyses below it is modeled as a “complex cognition” test based on the findings of Moore et al. [29].

Attention (ATT) measured by the Penn Continuous Performance Test (PCPT). This test [31] presents 7-segment displays of digits and letters mixed in with nonsense configurations for 300 ms each. A total of 180 stimuli are randomly presented at a rate of 1/s. The participant’s task is to press the space bar whenever the display forms a digit (for the first half of the test) or a letter (for the second half of the test).

Working Memory (WM) measured by the Penn Letter N-Back Test (LNB). In this test, participants attend to a continual series of letters that flash on the screen (one at a time) and press the spacebar according to three different rules (called the 0-back, 1-back, and 2-back). During the 0-back condition, the participant must respond to a currently present target (“X”). During the 1-back condition, the participant must press the spacebar when the letter on the screen is the same as the previous letter. During the 2-back condition, the participant must press the spacebar when the letter on the screen is the same as the letter before the previous letter (i.e., 2 letters back). In all trials, the interstimulus interval (ISI) is 2.5 s, and the stimuli (letters) themselves are presented for 0.5 s each. The participant practices all three principles before testing.

2.2.2. Episodic Memory

Verbal (Word) Memory (VME) measured by the Penn Word Memory Test (PWMT). This test [32] presents 20 target words that are then mixed with 20 foils equated for frequency, length, concreteness, and imageability. Participants are asked to memorize the target words as they are presented (5 s each), and after the presentation of the target words they are shown targets and foils and asked whether a word presented was included in the target list on a 1–4 scale (definitely yes; probably yes; probably not; definitely not).

Face Memory (FME) measured by the Penn Face Memory Test (PFMT). This test [32] presents 20 faces that are then mixed with 20 foils equated for age, sex, and ethnicity. The presentation paradigm is otherwise identical to the verbal and spatial memory tests.

Spatial Memory (SME) measured by the Visual Object Learning Test (VOLT). This test [33] uses Euclidean shapes as stimuli with the same paradigm as the word and face memory tests. A total of 10 shapes are presented 5 s each, and after the presentation of the target shapes participants are shown 10 targets and 10 foils and asked whether a shape presented was included in the target list on a 1–4 scale (definitely yes; probably yes; probably not; definitely not).

2.2.3. Complex Cognition

Language (Verbal) Reasoning (LAN) measured by the Penn Verbal Reasoning Test (PVRT). This test [28] consists of verbal analogy problems. A total of 15 trials are presented.

Nonverbal (Matrix) Reasoning (NVR) measured by the Penn Matrix Reasoning Test (PMAT). This test [29] consists of matrices requiring reasoning by geometric analogy and contrast principles. A total of 24 trials are presented, but the task stops if the participant makes 5 consecutive errors.

Spatial Processing (SPA) measured by the Penn Line Orientation Test (PLOT). This test [28] presents two lines at an angle, and participants mouse-click on a “button” that makes one line rotate until they consider it to have the same angle as the other. The relative location of the lines, their sizes, and the number of degrees of rotation with each click differ across trials. A total of 24 trials with short and long line lengths and 3, 6, or 9 degree rotation per click are presented.

IQ approximation by the Wide Range Achievement Test (WRAT). The WRAT-4 Word Reading subtest (used here) requires that participants read a list of phonetically regular and irregular words and, in the case of some lower ability participants, that they read a list of letters. Performance on this WRAT subtest serves as a proxy for premorbid IQ and neurocognitive functioning [34,35] that is relatively resistant to several forms of neurologic insult [36]. The WRAT estimates premorbid neurocognitive functioning by testing vocabulary and recognition of words.

2.2.4. Social Cognition

Emotion Identification (EID) measured by the Penn Emotion Identification Test (PEIT). This test [37] displays 40 faces (20 male, 20 female) expressing one of four emotions (happy, sad, anger, fear) and neutral faces, eight each. Faces are presented one at a time, and the participant selects the emotion displayed from five choices. The facial stimuli are balanced for sex, age, and ethnicity.

Emotion Intensity Differentiation (EDI) measured by the Penn Emotion Differentiation Test (PEDT). This test [28] presents pairs of emotional expressions, each pair from the same individual expressing the same emotion, one more intensely than the other or of equal intensity. Gradations of intensity were obtained by morphing a neutral to an emotionally intense expression, and the difference between pairs of stimuli ranged between 10% and 60% of mixture. The task is to click on the face that displays the more intense expression or indicate that they have equal intensity. The same emotions are used as for the PEIT, but the faces are different. A total of 36 trials are presented.

Age Differentiation (AGD) measured by the Penn Age Differentiation Test (PADT). This test [28] requires the participant to select which of two presented faces appears older, or if they are the same age. The stimuli were generated by morphing a young person’s face with that of an older person who has similar facial features. Stimuli vary by percent of difference in age (calculated based on the percentage contributed by the older face) and are balanced for sex and ethnicity. A total of 36 stimuli are presented.

2.3. Clinical Assessment: Structured Interview (GOASSESS)

The clinical assessment used in the PNC has been described in detail elsewhere [13,38]. Briefly, psychopathology was assessor-evaluated using a computerized, structured interview (GOASSESS), which was abbreviated and modified from the NIMH Genetic Epidemiology Research Branch Kiddie-SADS [39]. The interview included a timeline of life events, demographics and medical history, psychopathology screen, Children’s Global Assessment Scale (C-GAS) [40], and interviewer observations. GOASSESS assessed psychiatric and psychological treatment history and lifetime occurrence of major domains of psychopathology, including psychosis, mood (major depressive episode, manic episode), anxiety (generalized anxiety disorder, separation anxiety disorder, specific phobia, social phobia, panic disorder, agoraphobia, obsessive–compulsive disorder, post-traumatic stress disorder), attention deficit/hyperactivity disorder (ADHD), behavior (oppositional defiant disorder, conduct disorders), eating disorders (anorexia, bulimia), and suicidal thinking and behavior. Computerized algorithms assigned rankings reflecting DSM-IV categories of each psychopathology domain based on endorsement of contributing items by either the proband or collateral (behavioral domains), or by the proband (all other domains). Psychopathology categories were considered significant if sufficient symptoms were endorsed with frequency and duration approximating DSM-IV disorder or episode criteria, accompanied by significant distress or impairment rated ≥ 5 on an 11-point scale.

In addition, two screening tools to assess subthreshold psychosis spectrum symptoms were embedded within GOASSESS [38]. First, positive sub-psychotic symptoms were assessed using the PRIME Screen-Revised (PS-R) [41,42], which contains 12 items rated on a 7-point Likert scale (Extremely Disagree to Extremely Agree). PS-R Total Score is the sum of the 12 items. Second, negative/disorganized symptoms were assessed using six assessor-rated subscales of the Scale of Prodromal Symptoms (SOPS) from the Structured Interview for Prodromal Syndromes (SIPS v. 4.0) [43]: Avolition; Expression of Emotion; Experience of Emotions and Self; Occupational Functioning; Trouble with Focus and Attention; and Disorganized Communication.

Youth were categorized into the Psychosis Spectrum (PS) group at baseline if they endorsed any of the following: (a) possible or definite hallucinations or delusions based on K-SADS screen, with duration ≥1 day, occurring outside the context of substance, illness and medicines, and accompanied by significant impairment or distress (rating ≥ 5); (b) significant subthreshold psychosis symptoms on the PS_R; or (c) significant subthreshold/negative disorganized symptoms on the SOPS (see Calkins et al. [38] for full details).

The assessments were conducted by bachelor’s and master’s level assessors who underwent a rigorous 25 h training protocol developed and implemented by the second author, M.C. The training included didactic sessions, assigned readings, and supervised pairwise practice. To become certified for independent assessments, assessors had to undergo a standardized procedure requiring observation by a certified clinical observer who rated their proficiency on a 60-item checklist of interview procedures. Additionally, responses coded by the assessor in GOASSESS had to correspond to responses coded by a certified clinical observer. Assessors who did not achieve these standards were required to undergo repeat observation until passing criteria were met. To maintain quality, assessor drift was monitored through periodic review of audio-recordings of real interviews, and re-training and re-certification was conducted at the data collection mid-point. Assessors were assigned a maximum of 10 interviews per week, with the goal of completing 5–7 interviews weekly. The quality of interview data was assured through a computerized error-checking algorithm and a standardized post-administration review process by certified clinical reviewers.

2.4. Neighborhood Characteristics

The neighborhood SES score calculation is described in Moore et al. [44]; briefly, participant addresses were converted to geocodes and linked to census block-groups (neighborhoods). Data about these neighborhoods were pulled from the American Community Survey (e.g., median income, percent married, percent of lots that are vacant, etc.), and summary scores (including SES) were estimated from this data using factor analysis. The strongest indicators (and loadings) of this SES factor (from Moore et al. [44], Table 1, F1 in two-factor solution) were percent married (0.84), percent in poverty (−0.86), median family income (0.82), percent with high school diploma (0.74), and population density (−0.71).

2.5. Intracranial Volume (ICV)

Total ICV was obtained from the PNC neuroimaging protocols described in [45]. Neuroimaging data were available for 1628 participants. Because the focus of the current project makes detailed neuroimaging analyses beyond the scope, we opted to use the most basic overall measure, ICV. Previous research has demonstrated that ICV is associated with various measures of cognitive performance with moderate effect size [46,47,48]. Note that it is more common in contemporary imaging studies (including some cited above) to report total brain volume (TBV) rather than ICV. However, as shown in Supplementary Figure S1, TBV and ICV correlate almost perfectly. We therefore opted to report the simpler measure (ICV), because it can be obtained from computerized tomography and skull-based anthropometric measurements, whereas TBV cannot. There are also image quality considerations involved in acquiring TBV, which is why Figure S1 shows data for N = 1568 rather than the full N = 1628 who have ICV.

2.6. Longitudinal Psychosis Assessment

Longitudinal PS change was obtained from follow-up data in the PNC, which included subsequent assessments of PS symptoms [2]. Specifically, N = 642 participants from the PNC were followed up using a custom protocol consisting of modules of the K-SADS, the Structured Interview for Prodromal Syndromes (version 4.0) [49], the psychotic and mood differential diagnosis modules (C/D), and substance use module (E) of the Structured Clinical Interview for DSM-IV [50]. Time difference between the first and last assessment ranged from 0.2 to 9.3 years (mean = 4.52 years). On average, participants completed 2.75 visits (age range first visit = 8.1–21.9; age range final visit = 9.5–29.9). Individuals were classified as meeting psychosis spectrum criteria at follow-up if they had either (a) a DSM-IV psychotic disorder or mood disorder with psychotic features or (b) at least one Scale of Prodromal Symptoms positive symptom currently (past 6 months) rated 3–5, or at least two negative and/or disorganized symptoms rated 3–6. This group was divided into two groups for analysis: those who did and those who did not endorse baseline PS symptoms sufficient to be categorized as PS [38]. These baseline categories were then further divided into two categories each. Those who entered as PS were divided into those who remained PS at follow-up (“Persistent”) and those who did not meet criteria at follow-up (“Resilient” [2]). Those who were classified as non-PS at baseline were split into those who met PS criteria at follow-up (“Emergent”) and those who remained non-PS at follow-up (“TD” for “typically developing”). As part of validating the “c” factor, scores on the “c”, “p”, and “g” factors were compared between the Persistent and Resilient groups, and (separately) between the Emergent and TD groups.

2.7. Statistical Analysis

The first step in analysis was to estimate the structural model for “c”, which was a confirmatory tri-factor model combining the bifactor structures for “g” and “p”. Figure 1 shows the model configuration comprising “c”, “p”, “g”, and all specific sub-factors, where all factors in the model are orthogonal to each other. Configuration for the “g” factor components was taken from Moore et al. [29], and the “p” factor configuration was guided by Calkins et al. [13] with some adjustments. Both 2015 studies were conducted on the same sample (PNC), allowing much of the “c” factor structure to be known a priori. This is somewhat unusual insofar as factor analytic studies often begin with exploratory factor analysis, followed by confirmation of the structure (preferably in a different sample) using confirmatory factor analysis (CFA); however, because the structure of these cognitive tests and clinical diagnoses is known [2,29], we were able to begin at the CFA stage.

To explore the effect of age on the structure of the “c” factor model, we also conducted the above analyses on participants aged 8–12 and 13–21 separately. We compared coefficient estimates and model fit indices across these two models.

The CFA for “c” was conducted in Mplus (v8.4) [51] using the mean- and variance-adjusted weighted least squares (wlsmv) estimator. Model fit was assessed using the comparative fit index (CFI; >0.90 acceptable), root mean-square error of approximation (RSMEA; <0.08 acceptable), and standardized root mean-square residual (SRMR; <0.08 acceptable) [52]. Due to the “Executive” and “Motor” specific factors having only two indicators each (where three are required for identification in a bifactor model), factor loadings within these factors were constrained to equality. That is, the loadings of attention and working memory on the Executive factor were constrained to be equal to each other, and the same was true of the tapping and motor praxis tasks on the Motor factor.

Finally, criterion validity of the c-factor scores was assessed by comparing its relationship with external criteria with the same relationships using “p” and “g”. The specific validity criteria were average parent education, neighborhood socioeconomic status (SES), global assessment of functioning (GAF), and total intracranial volume (ICV). To assess the utility of the c factor in predicting functional outcome, we examined its association with longitudinal psychosis spectrum (PS) change at follow-up. Please see the Supplementary Materials for more discussion and rationale for using these specific validity criteria.

Relationships with continuous criteria were assessed by Pearson correlations, all of which were expected to be positive (higher “c”, higher SES/GAF/ICV/parent education); mean differences between follow-up groups (longitudinal PS change) were assessed using t-tests. All correlations and t-tests were performed using “p” and “g” scores both from a “c” factor model and in a model without a “c” factor. In the model including the “c” factor, “p” and “g” include only variance not already explained by “c”, so they are akin to residuals of “p” and “g” after controlling for “c”. We therefore also included “p” and “g” scores estimated without “c” to examine how strongly they associate with criteria when not controlled for “c”.

3. Results

Table 2. Confirmatory “c” factor loadings from tri-factor model comprising “c”, bifactor general factors “p” and “g”, and specific sub-domain factors.

Super-Domain	Specific Factor	Test	Specific Factor	Bifactor General (“p” for Clinical; “g” for Cognitive)	“c” Factor
Clinical	Anxious-Misery	Depression	0.353	0.707	0.029
		Generalized	0.623	0.482	0.010
		OC	0.296	0.620	0.004
		Separation Anx.	0.340	0.366	0.039
		Panic	0.350	0.558	−0.031
		PTSD	0.175	0.533	−0.176
	Psychosis	PS-R	0.344	0.406	−0.169
		Halluc./Delus.	0.270	0.625	−0.156
		Mania	−0.157	0.596	−0.133
	Phobias	Specific Phob.	0.411	0.386	−0.044
		Social Phob.	0.305	0.517	−0.167
		Agoraphobia	0.334	0.618	−0.245
	Externalizing	ADH	0.401	0.263	−0.211
		OD	0.814	0.520	−0.246
		Conduct	0.510	0.454	−0.308
Cognitive	Executive	Attention	0.415	0.331	0.258
		Working Mem.	0.411	0.236	0.393
	Memory	Verbal Mem.	0.272	0.505	0.231
		Face Mem.	0.329	0.574	0.201
		Spatial Mem.	0.358	0.441	0.188
	Complex	Mental Flex.	0.246	0.230	0.454
		Language	−0.086	0.236	0.736
		Nonverbal	0.295	0.254	0.521
		Spatial (Line)	0.222	0.279	0.461
		WRAT	−0.211	0.063	0.698
	Social	Emotion ID	0.140	0.581	0.290
		Emotion diff.	0.583	0.420	0.483
		Age Diff.	0.398	0.454	0.261
	Motor	Motor (TAP)	0.355	0.281	0.219
		Mouse Praxis	0.349	0.501	0.146

Note. Bolded loadings are significant at p < 0.05 level; Generalized = generalized anxiety; OC = Obsessive–Compulsive; Anx. = anxiety; PS-R = PRIME Screen-Revised; Halluc. = hallucinations; Delus. = delusions; Phob. = phobia; ADHD = Attention-Deficit Hyperactivity; OD = Oppositional–Defiant; Dis. = disorder; Mem. = memory; Flex. = flexibility; ID = identification; diff. = differentiation; TAP = finger-tapping.

shows the factor loadings from the “c” factor model, including specific, bifactor general (“p” and “g”), and “c” itself. Fit of the model was acceptable: CFI = 0.98, RMSEA = 0.021 ± 0.001, and SRMR = 0.030. Interpretation of the specific factor loadings is the correlation between the indicator and the factor after controlling for the covariance explained by “c” and the bifactor general factors. Of the specific factors, Externalizing (mean loading = 0.58) and Executive (mean loading = 0.41) had the strongest loadings, indicating moderate inter-variable covariance was left over even after accounting for “g”, “p”, and “c”. The opposite was true for Complex Reasoning (mean absolute loading = 0.21) and Psychosis (mean absolute loading = 0.26), which were weak due to most of their inter-variable covariance being explained by the super-ordinate “g”, “p”, and “c” factors.

The bifactor general factor (“p” and “g”) loadings indicate the inter-variable covariance remaining after controlling for “c” only. The “p” factor was overall more strongly determined (mean loading = 0.51) by its indicators than was “g” (mean loading = 0.36). Within the “p” factor, the strongest indicators were Depression (0.71) and the Hallucination/Delusion screen (0.63), followed closely by OC (0.62) and agoraphobia (0.62); within the “g” factor, the strongest indicators were Emotion Identification (0.58) and Face Memory (0.57). Finally, the strongest indicators for the “c” factor (comprising all variables) were Language (0.74), WRAT (0.70), Nonverbal (matrix) Reasoning (0.52), Emotion Differentiation (0.48), and Line Orientation (0.46). The strongest clinical indicators of “c” were Conduct (−0.31), Oppositional–Defiance (−0.25), and Agoraphobia (−0.25).

Supplementary Table S2 shows the results of the “c” factor model estimated separately in participants aged 8–12 years and 13–21 years. Fit of both models was acceptable; for the younger and older groups, respectively, CFI = 0.98 for both, RMSEA = 0.023 and 0.019, and SRMR = 0.042 and 0.033. Measurement invariance was assessed by comparing the fit of a multiple-group CFA when loadings and intercepts were freely estimated in each age group to the same CFA when loadings and intercepts are constrained to be equal in the two age groups. Following the guidelines suggested by Chen et al. [53], the differences between these models’ RMSEAs (0.003) and SRMRs (0.009) suggest measurement invariance has been satisfied, while the difference between their CFIs (0.011) suggests a possible invariance violation. Examining the loadings in Table S2, where all with absolute value > 0.40 are highlighted, we see there is some variation between age groups in the specific and bifactor general loading patterns. However, the pattern of loadings in the “c” factors are quite similar, with the pattern of the most salient loadings (abs. value > 0.40) being identical between the younger and older groups.

Figure 2 shows the relationships between four validity criteria and the “c”, “g”, and “p” factors, where “p” and “g” come from a model that also includes “c”. All effects were in the expected direction, with “c” and “g” correlating positively and “p” correlating negatively with all criteria. For parent education, neighborhood SES, and ICV (panels a, c, and d), the largest effect was for the “c” factor, with correlation (r) values of 0.43, 0.47, and 0.39, respectively. For the GAF (panel c), the largest effect was found for the “p” factor (r = −0.43), followed by the “c” factor (0.27).

Figure 3 shows the mean comparisons of each factor score for the longitudinal PS groups. Among those who met PS criteria at baseline (panel a), those who also met criteria at follow-up (Persistent) scored significantly lower on the “g” and “c” factors at baseline, and significantly higher on the “p” factor at baseline (all p < 0.05). The largest effect (d = 0.30) was for “c”. Among those who did not meet PS criteria at baseline (panel b), those who remained non-PS at follow-up scored significantly higher on the “g” and “c” factors and significantly lower on the “p” factor at baseline (all p < 0.05). Again, the largest effect (d = 0.57) was for “c”. Finally, Supplementary Table S1 shows the results of the same analyses shown in Figure 2 and Figure 3 but including the “p” and “g” factor scores calculated without the “c” factor, i.e., without the “c” factor regressed out of them. These results are discussed in further detail in the Supplemental Information.

4. Discussion

This study offers the first step in demonstrating the potential utility of estimating a “c” factor in a community sample when both cognitive and psychopathology variables are measured. The tri-factor structural measurement model fit the data well, and the scores generated from the model associate with external criteria in expected directions. Furthermore, the “c” factor based on cross-sectional data helped predict the clinical outcome in a subsample that was followed longitudinally. There is some evidence that the “c” factor captures additional signals provided by the cognitive and psychopathology variables that might not be captured by each super-domain (“p” and “g”) alone. Further, there is moderate evidence that measurement invariance across age is achieved, at least within this 8–21 year age range.

The reasons for the existence of “c”—i.e., its mechanisms and origin—are unclear, but some explanations can be offered. From a mechanistic point of view, Fissler et al. [23] propose mitochondrial bioenergetics as a central process underlying “c”, based on previous studies linking mitochondrial function to both “g” [54,55] and “p” [56,57]. Because the brain accounts for 20% of the energy consumption in the body [58], and mitochondria are responsible for energy production [59], mitochondrial dysfunction may lead to adverse outcomes in anything the brain does, which includes the broad range of behaviors that can be characterized as psychopathology or cognition. Unfortunately, data on mitochondrial functioning were not available in this data set, so testing this theory was not possible here. However, there is evidence for mitochondrial involvement in schizophrenia, which is high on “p” and low on “g”. In the recurrent rare copy number variant (CNV) associated with chromosome 22q11.2 deletion, where there is about a 25-fold increased rate of schizophrenia compared to the general population [60], six of the deleted genes encode proteins that localize to mitochondria. Deficits in iPSC-derived neurons from patients with 22q11.2 deletion syndrome are evident in those with schizophrenia compared to those without [61]. Furthermore, an increase in mitochondrial biogenesis and function was associated with the absence of schizophrenia in neurons derived from lymphoblastic cell lines of individuals with 22q11.2 deletion syndrome and was reversible by agents that enhance mitochondrial biogenesis [62].

A functional explanation for “c” is offered by proposing a general “fitness” factor [63,64,65], where fitness is defined in the adaptationist (evolutionary) sense: a set of characteristics that enhance the probability of survival and reproduction of an individual. Several physiological indicators of fitness have been proposed in humans, including muscularity in men [66], vocal characteristics [67,68], handgrip strength in men [69], facial characteristics [70,71], and (lack of) fluctuating asymmetry [72,73], among others. Possibly unique to humans, however, is the evidence for mental/psychological fitness indicators, such as humor [74], general intelligence [75], artistic virtuosity [76], vocabulary size [77], moral signaling [78], and even subclinical characteristics of schizophrenia [79], bipolar disorders [80], and autism [81]. Furthermore, these physiological and psychological fitness indicators overlap in the expected direction, where positive physiological indicators tend to correlate with positive psychological indicators [82,83], suggesting the possibility of a single factor underlying both. Note that these “fitness indicators” are themselves explained to varying degrees by the overlapping theories of classical evolution [84], sexual selection [85], and developmental instability [86,87], but here we present them only as examples of mental characteristics (such as those captured in “c”). In the present study, we do find some evidence supporting the “fitness indicator” explanation for “c”. Specifically, if “c” indicates fitness in the way described above, we would expect cognitive tests with the highest factor loadings on “c” to be those typically most associated with “g” [65], and that is what we find. All three of the tests with loadings > 0.50 on “c” (PMAT, PVRT, and WRAT), measure domains (matrix reasoning and verbal ability, including analogies) consistently reported as central to “g” [17,88,89].

Practical applications of the “c” factor depend on results of future research, but we propose some examples here. If indeed “c” contains information not captured by either “g” or “p”, as tentatively suggested by results using the validity criteria above, it offers a single measure helpful to predict or explain outcomes. In studies that do not focus on either cognition or psychopathology, “c” could function as a useful covariate. For example, in a study relating blood pressure to dietary habits, it would make sense to control for brain (dys)function without having to include multiple covariates. Second, as alluded to by Fissler et al. [23], the “c” factor model allows one to examine associations of “p” and “g” with other criteria after controlling for “c”. In the same way as the “p” factor model allows one to control for “p” in examining relationships with the specific factors (e.g., depression, externalizing, etc.), the “c” factor allows one to do the same with “p” and “g”. Further, because the “c” factor is modeled in an orthogonal tri-factor configuration, all factors in the model can be related simultaneously to an external criterion without concern for collinearity. Third, “c” could be useful in tracking the overall brain function of participants in a clinical trial. For example, in a Phase 1 study where side effects are of central concern, the “c” factor could be a way to assess participants’ day-to-day or week-to-week functioning and brain health as the protocol proceeds. Finally, the relative sizes of the standardized loadings of the “c” factor model itself can be helpful in informing (1) which measures to prioritize if one is planning a study that involves measuring overall cerebral function but is limited in available time to do so, or (2) in a data set that is already collected, which measures would be the best for measuring overall cerebral functioning in a composite score. Based on the present study, if interested in “c”, one would want to prioritize or focus on measures of IQ (as indicated by high loadings on matrix reasoning and analogies) and clinical assessments of externalizing disorders and agoraphobia. However, we discourage using this single study as the basis for either #1 or #2 above; further research on the “c” factor is necessary.

This study has some notable limitations that warrant careful consideration. First, clinical diagnostics were assessed using a mix of self- and parent-reported information, depending on the age range (e.g., all parent-reported for participants 8–10 years old), and there is evidence of only moderate agreement between parents and children in this sample [90]. Parent-reporting was used only for children under 11 because there were fewer externalizing than internalizing disorders assessed here, and there is evidence that parent-reported data are more valuable for externalizing symptoms [91]. This methodological choice may have introduced systematic measurement error that could affect the interpretation of developmental patterns in our findings. Relatedly, in this developmental age range of 8- to 21-year-olds, it is possible the “c” factor has not had sufficient time to manifest, or perhaps its cognitive and clinical indicators manifest on different time scales. This developmental timing issue raises important questions about the nature of “c” itself—i.e., if cognitive and clinical manifestations emerge asynchronously, this could suggest that “c” is not a unitary construct but rather a developmental process that unfolds over time. More insight could be gained from future studies using a larger age range, particularly if these studies can track the emergence and stability of “c” across different developmental periods. A third limitation is that the sample used here was mostly cross-sectional, with only a small proportion used in longitudinal analysis. Most of this longitudinal sub-sample included only two time points, which fundamentally limits our ability to draw causal inferences and test alternative theories about how “c” arises. For example, because of the well-established links among perception, cognition, and psychopathology [92,93], it is possible that negative events give rise to negative thoughts, which give rise to negative affect, and so on, with the opposite also occurring (positive events → positive affect), making “c” a construct that arises only longitudinally given individual differences in experience. This theoretical model suggests that “c” might be better conceptualized as an emergent property of recursive cognitive-affective processes rather than a stable trait. More longitudinal data would allow testing of such a theory in comparison to other theories discussed above, such as whether (1) “c” represents a stable individual difference factor that influences the interpretation of events, or (2) “c” emerges from the cumulative effects of experience on neural development. Nonetheless, the validation of “c” with longitudinal clinical outcomes in this study suggests that it may be useful for predicting clinical outcomes beyond its cross-sectional explanatory power. Finally, it is worth noting that the “p” factor of psychopathology, a central component of “c”, has some limitations that directly impact our theoretical framework [94,95,96]. Chief among these are that (1) the consistently superior fit indices of bifactor models of “p” (or anything) are not evidence that the bifactor configuration is “true” because the bifactor model is less parsimonious than competing models, and (2) theories of why the “p” factor exists (if it does) are weak, difficult to falsify, or not rigorously tested against alternative explanations for the “positive manifold” of psychiatric symptoms. These methodological and theoretical concerns suggest that our conceptualization of “c” may need substantial revision if the underlying “p” factor proves to be an artifact of measurement rather than a meaningful construct. Perhaps despite the acceptable fit of bifactor and higher-order models of psychopathology, the relationships among symptoms are better modeled by alternative approaches, such as network models [97], which would suggest that “c” might be better understood as an emergent property of interconnected cognitive-clinical networks rather than a latent factor. If this is true of the “p” factor, the conceptualization of the “c” factor presented here would need fundamental modifications to align with a network-based understanding of psychopathology. Despite these limitations and their theoretical implications, the present study provides some new insight into the feasibility of using a “c” factor in large-scale studies. The findings further suggest that “c” factor scores may be a psychometrically efficient way to capture overall cerebral function, but alternative theoretical frameworks may ultimately prove more useful for understanding the complex relationships between cognition and psychopathology.

The relationships we observed between the “c” factor and our validation criteria provide preliminary support for both the mitochondrial and fitness indicator theories of its underlying mechanism. The strong association between “c” and intracranial volume (r = 0.39) aligns with the mitochondrial hypothesis, as brain size and energy consumption are closely linked; the brain consumes approximately 20% of the body’s energy despite comprising only 2% of its mass [58], suggesting that larger brains may require more efficient mitochondrial functioning. The robust correlations between “c” and both socioeconomic indicators (parent education r = 0.43; neighborhood SES r = 0.47) could support either theoretical framework; from a mitochondrial perspective, higher SES environments may promote better mitochondrial function through improved nutrition, reduced environmental stressors, and better access to healthcare; from a fitness indicator perspective, these correlations suggest the kind of positive manifold across different domains that would be expected if “c” represents overall genetic quality. Note it is difficult to say what the higher end of genetic “quality” means here. Strictly speaking, “high-quality” genes are simply genes that built humans who were especially good at reproducing in our ancestral environment. And as discussed above, sexual selection likely played a role, in which case “high-quality” simply means desirable to the opposite sex. Regardless, it is easier to imagine what “low-quality” genes might be, including systematic phenomena like deletions and duplications, as well as de novo mutations with deleterious effects. Perhaps most telling is the predictive relationship between “c” and longitudinal psychosis outcomes (d = 0.30–0.57), as both theoretical frameworks would predict such prognostic utility. Mitochondrial dysfunction has been implicated in psychosis progression (as evidenced by our findings in 22q11.2 deletion syndrome), while the fitness indicator framework would expect more severe psychopathology to emerge in individuals with lower overall genetic quality. The association between “c” and global functioning (r = 0.27) similarly supports both perspectives, as both frameworks would predict that higher “c” scores indicate better overall system integrity, whether measured through mitochondrial efficiency or genetic quality. While our data cannot definitively adjudicate between these theoretical explanations, the consistent pattern across multiple domains suggests these mechanisms may operate in parallel rather than being mutually exclusive. Future research should focus on directly testing these proposed mechanisms through several approaches. First, longitudinal studies incorporating direct measures of mitochondrial function (e.g., through magnetic resonance spectroscopy or peripheral biomarkers) could help establish whether mitochondrial efficiency mediates the relationship between “c” and clinical outcomes. Second, genetic studies examining polygenic scores for both mitochondrial function and overall genetic quality could help disentangle these mechanisms. Additionally, intervention studies targeting mitochondrial function through lifestyle modifications (e.g., diet, exercise) or pharmacological approaches could provide causal evidence for this mechanism if they successfully improve “c” scores.

This study’s findings have several important clinical implications. First, the robust associations between “c” and both concurrent functioning and longitudinal outcomes suggest that assessing cognitive and clinical symptoms together, rather than separately, may provide clinicians with better prognostic information. This is particularly relevant for early intervention services, where the “c” factor could help identify individuals at highest risk for persistent psychosis spectrum symptoms, given its stronger predictive value compared to either “p” or “g” alone. Second, the hierarchical structure revealed by the “c” factor model suggests that interventions targeting overall cerebral functioning (e.g., aerobic exercise, sleep optimization, or cognitive remediation) might have broader benefits across both cognitive and clinical domains than previously recognized. Third, the strong loadings of specific indicators on “c” (particularly language ability, WRAT performance, and nonverbal reasoning) provide clinicians with efficient screening tools that could help identify patients who might benefit from more comprehensive evaluation. Fourth, the possible strong connection to energy metabolism suggests that metabolic health should be a key consideration in mental health treatment, potentially opening new avenues for intervention (e.g., nutritional supplements). Finally, the findings support a more integrated approach to treatment planning, where cognitive and clinical symptoms are conceptualized as interrelated manifestations of cerebral functioning rather than separate domains requiring independent interventions. This could lead to more holistic treatment strategies that address both cognitive and clinical symptoms simultaneously.

5. Conclusions

The successful modeling of a “c” factor in this large community sample demonstrates its potential utility in capturing overall cerebral function across cognitive and psychopathology domains, and it appears to fulfill the measurement invariance assumption across age groups. The “c” factor’s associations with external criteria and its ability to predict longitudinal clinical outcomes suggest it may offer additional insights beyond traditional “g” and “p” factors, potentially advancing our understanding of brain function and informing future research and clinical applications. Future studies including combinations of cognitive and clinical measures can attempt to estimate a “c” factor to further refine its definition, confirm the relative importance of its indicators, and determine the extent of its validity.